9000034909
Level:
B
Find the solution set of the following quadratic inequality.
\[
-3(x + 2)^{2} < 0
\]
\(\mathbb{R}\setminus \{ - 2\}\)
\(\emptyset \)
\(\{- 2\}\)
\(\mathbb{R}\)
B
9000034910
Level:
B
Find the solution set of the following quadratic inequality.
\[
(x - 3)^{2}\geq 0
\]
\(\mathbb{R}\)
\(\emptyset \)
\(\mathbb{R}\setminus \{3\}\)
\(\{3\}\)
9000035003
Level:
B
The tree of the height \(12\, \mathrm{m}\)
is observed from the place horizontal with the base of the tree. The angle of elevation
is \(10^{\circ }\).
Find the distance of the observer from the base and round to the nearest meters.
\(68\, \mathrm{m}\)
\(2\, \mathrm{m}\)
\(12\, \mathrm{m}\)
\(48\, \mathrm{m}\)
9000035008
Level:
B
Sun shines to the road at the angle \(53^{\circ }22'\).
An electric column near the road casts the shadow of the length
\(4.5\, \mathrm{m}\). Find
the height of the column and round your answer to the nearest meters.
\(6\, \mathrm{m}\)
\(3\, \mathrm{m}\)
\(4\, \mathrm{m}\)
\(5\, \mathrm{m}\)
9000035009
Level:
B
Two forces act on the body at one point. The force
\(F_{1} = 760\, \mathrm{N}\)
acts horizontally from left to the right and the force
\(F_{2} = 28.8\, \mathrm{N}\) acts
vertically from the top to the bottom. Find the angle between the horizontal direction
and the direction of the resulting force and round your answer to the nearest degrees
and minutes.
\(2^{\circ }10'\)
\(3^{\circ }10'\)
\(2^{\circ }20'\)
\(3^{\circ }20'\)
9000035010
Level:
B
The height of a right trapezoid is \(4\, \mathrm{cm}\).
The length of the longer base is \(7\, \mathrm{cm}\)
and the angle between this base and the leg of the trapezoid is
\(52^{\circ }\). Find
the perimeter of the trapezoid and round to the nearest centimeters. See the picture with a right trapezoid.
\(20\, \mathrm{cm}\)
\(18\, \mathrm{cm}\)
\(19\, \mathrm{cm}\)
\(21\, \mathrm{cm}\)
9000035001
Level:
B
The angle of elevation of a straight road is \(3^{\circ }30'\).
The distance between two places measured along the road is
\(2\, \mathrm{km}\). For these places, find the difference in altitudes, i.e. the vertical distance, and round the result to the nearest meter. (See the picture.)
\(122\, \mathrm{m}\)
\(276\, \mathrm{m}\)
\(98\, \mathrm{m}\)
\(49\, \mathrm{m}\)
9000035007
Level:
B
A roof gable has the shape of an isosceles triangle with the base of \(14\, \mathrm{m}\).
The angle between the roof and the horizontal direction is
\(31^{\circ }\). Find the height of the gable. Round your result to one decimal place.
\(4.2\, \mathrm{m}\)
\(5.9\, \mathrm{m}\)
\(3.6\, \mathrm{m}\)
\(11.2\, \mathrm{m}\)
9000035606
Level:
B
Find the quadratic equation with real valued coefficients and one of the solutions
\(x_{1} = -1 + \mathrm{i}\sqrt{3}\).
\(x^{2} + 2x + 4 = 0\)
\(x^{2} - 2x + 4 = 0\)
\(x^{2} + 2x - 4 = 0\)
\(x^{2} - 2x - 2 = 0\)
\(x^{2} + 2x + 2 = 0\)
9000035605
Level:
B
The number \(\cos \frac{7}
{6}\pi + \mathrm{i}\sin \frac{7}
{6}\pi \)
is a solution of a quadratic equation with real valued coefficients. Find the second
solution.
\(\cos \frac{5}
{6}\pi + \mathrm{i}\sin \frac{5}
{6}\pi \)
\(\cos \frac{1}
{6}\pi + \mathrm{i}\sin \frac{1}
{6}\pi \)
\(\cos \frac{7}
{6}\pi + \mathrm{i}\sin \frac{7}
{6}\pi \)
\(\cos \frac{11}
{6} \pi + \mathrm{i}\sin \frac{11}
{6} \pi \)